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Article Assessing the Energy Resilience of Office Buildings: Development and Testing of a Simplified Metric for Real Estate Stakeholders

Paul Mathew * , Lino Sanchez, Sang Hoon Lee and Travis Walter

Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA; [email protected] (L.S.); [email protected] (S.H.L.); [email protected] (T.W.) * Correspondence: [email protected]

Abstract: Increasing concern over higher frequency extreme weather events is driving a push towards a more resilient built environment. In recent years there has been growing interest in understanding how to evaluate, measure, and improve building energy resilience, i.e., the ability of a building to provide energy-related services in the event of a local or regional power outage. In addition to human health and safety, many stakeholders are keenly interested in the ability of a building to allow continuity of operations and minimize business disruption. Office buildings are subject to significant economic losses when building operations are disrupted due to a power outage. We propose “occupant hours lost” (OHL) as a means to measure the business productivity lost as the result of a power outage in office buildings. OHL is determined based on indoor conditions in each space for each hour during a power outage, and then aggregated spatially and temporally to determine the   whole building OHL. We used quasi-Monte Carlo parametric energy simulations to demonstrate how the OHL metric varies due to different building characteristics across different climate zones and Citation: Mathew, P.; Sanchez, L.; seasons. The simulation dataset was then used to develop simple regression models for assessing the Lee, S.H.; Walter, T. Assessing the Energy Resilience of Office Buildings: impact of ten key building characteristics on OHL. The most impactful were window-to-wall ratio Development and Testing of a and window characteristics. The regression models show promise as a simple means to assess and Simplified Metric for Real Estate screen for resilience using basic building characteristics, especially for non-critical facilities where it Stakeholders. Buildings 2021, 11, 96. may not be viable to conduct detailed engineering analysis. https://doi.org/10.3390/ buildings11030096 Keywords: energy resilience; resilience metrics; building habitability; passive survivability; office buildings Academic Editor: Ravi Srinivasan

Received: 17 December 2020 Accepted: 24 February 2021 1. Introduction Published: 5 March 2021 Resilience in the context of the built environment is commonly described as the ability to prepare for and adapt to changing conditions and withstand and recover rapidly Publisher’s Note: MDPI stays neutral from disruptions [1]. Increasing concern over higher frequency extreme weather events with regard to jurisdictional claims in is driving a push towards a more resilient built environment. In recent years there has published maps and institutional affil- iations. been growing interest in understanding how to evaluate, measure, and improve building energy resilience, i.e., the ability of a building to provide energy-related services in the event of a local or regional power outage caused by or coupled with events such as extreme heat and cold, wildfires, , hurricanes, and floods [2,3]. Energy-related services include the provision of lighting, heating, ventilation and air conditioning (HVAC), and Copyright: © 2021 by the authors. plug power. The building design community is looking to address these issues in new and Licensee MDPI, Basel, Switzerland. retrofit construction; owners and operators need to assess and improve the energy resilience This article is an open access article of their buildings, and private-sector intermediaries such as the insurance industry are distributed under the terms and conditions of the Creative Commons financially vulnerable to these impacts and are potential partners in loss mitigation [4]. Attribution (CC BY) license (https:// Even in developed countries with a mature and reliable electrical grid, many buildings creativecommons.org/licenses/by/ are subject to power outages due to extreme events. For example, millions of people 4.0/). in California were affected by power outages lasting several days due to wildfires that

Buildings 2021, 11, 96. https://doi.org/10.3390/buildings11030096 https://www.mdpi.com/journal/buildings Buildings 2021, 11, 96 2 of 20

triggered a precautionary shutdown of some transmission lines. Similarly, extreme winter weather and ice storms in many parts of the United States periodically cause days-long power outages for homes and businesses. Energy resilience is a critical component of overall building resilience, and is distinct from structural resilience, or resilience against human-created threats. Human safety and health are naturally the first priority driver for resilience. Beyond that, many stakeholders are keenly interested in the ability of a building to provide a safe and comfortable indoor environment to allow continuity of operations and minimize business disruption. Buildings such as offices, retail, food service, and sales, while not mis- sion critical like hospitals and public safety buildings, are subject to significant economic losses should building operations be halted due to a power outage. Financial losses due to disrupted business functions may outweigh any costs associated with structural damage. This was the case for numerous buildings after Hurricane Sandy, where insurance pay- ments for lost business were generally more significant than reconstruction expenses [5,6]. These considerations are increasing the interest in energy resilience from building owners, operators, and insurers. One of the primary challenges with energy resilience is that this concept is still loosely defined and not well characterized. Resilience is sometimes presented in tandem with large- scale sustainability efforts [7]. Numerous standards and guidelines for occupant comfort and energy efficiency already exist [8], including through the LEED (Leadership in Energy and Environmental Design) rating system’s passive survivability credit [9]. However, there are no widely-accepted aggregate metrics for energy resilience. This paper proposes a simple aggregate metric that serves as a first-order measure of building energy resilience, especially as it relates to business continuity in commercial buildings such as offices. We first provide a background of the relevant literature. Next, we define and describe the proposed metric. We show the application of the metric in a parametric energy sim- ulation analysis. We then describe the viability of computing the metric based on easily obtainable building features. We conclude with limitations and areas for further research.

2. Background Much of the literature on building-level metrics for resilience is focused on the conti- nuity of building operations for whole communities during a disruption or disaster [10–12]. The literature on energy resilience indicates that there are currently no universally agreed- upon metrics for assessing the energy resilience of individual buildings [13]. Various conceptual frameworks have been developed as methods for strategically organizing rel- evant resilience priorities and data requirements to inform the most appropriate metrics for determining resilience, including matrices [14], workflow charts [15], and decision trees [16]. However, while these frameworks offer stakeholders an approach to thinking through the process of resilience measurement, they do not include explicit energy re- silience metrics for individual buildings. A resilience index developed by [17] quantifies the resilience of a building as a function of “robustness, resourcefulness, and recovery” within the context of maintaining building functionality when faced with unique hazards. An “energy provision” metric developed by [18] assesses the ability of a building to pro- vide energy during a disruption, with more specific metrics including natural/mechanical ventilation potential, air filtration, and daylight coverage. Criteria-based building resilience and sustainability rating systems and certifications, such as LEED [19], RELi 2.0 [20], US Resiliency Council Building Rating System [21], and BREEAM (Building Research Estab- lishment Environmental Assessment Method) [22] aim to assess building resilience mostly through “feature-based” verification [23], which provides a prescriptive path to resilience, but does not necessarily take the form of explicit resilience metrics. A key concept emerging in building energy resilience is “passive survivability”, which denotes the ability of buildings to keep occupants safe and comfortable during a power outage [24]. “Thermal autonomy” has been proposed to assess a building’s potential to keep occupants at acceptable temperatures, with the metric ultimately consisting of Buildings 2021, 11, 96 3 of 20

the time occupants are kept in these sufficient thermal conditions [24,25]. Similarly, as another time-based metric, “hours of safety” has been proposed as a metric to assess the potential of a building to keep people safe from extreme cold and heat during a power outage, attributing resilience to the performance of -associated building components, such as insulation [26]. Other approaches for measuring building energy resilience is to group buildings with infrastructure systems by their role in infrastructural resilience [11]. Buildings are viewed as components of the larger power grid system, contributing to grid resilience, citing building energy resilience as a function of grid-connectivity [27]. While metrics used to assess the infrastructural resilience of the built environment may not focus on energy explicitly, considerations for measuring the capacity of key facilities, such as hospitals and hotels, to serve and offer shelter to people in times of need, may have embedded energy resilience implications by looking to the continued functionality of these facilities during power disruptions and grid failure. The GridOptimal metrics proposed by the New Buildings Institute address power availability for buildings, but with a stronger emphasis on the contribution of energy-efficient buildings to the overall efficiency of the grid, with a decarbonized grid as the primary focus [28], and not necessarily the comfort and safety of occupants at the individual-building level. Focusing on the economic implications of lost access to grid energy for individual buildings, “value of lost load” (VoLL) is proposed as a metric to assess the financial consequences of a power disruption, where a lower VoLL, expressed as “$/kWh”, denotes a lesser degree of financial consequence due to a loss in load served, thus indicating a greater degree of building energy resilience [13]. Similarly, “percent of critical load system can support” is proposed as a metric to quantify the amount of lost grid electricity that can be made up by resilience measures during a power disruption, especially renewable energy systems [29,30]. These metrics are primarily focused on renewable energy as a means to foster building energy resilience and are not easily applicable to passive building features. Certain passive building features, such as external shading and high-performing windows, have shown to have significant potential in mitigating indoor conditions in extreme events [31], but further research is still needed to demonstrate the role of these passive building features as a means to increase energy resilience [32]. Our review suggests that resilience, even when narrowed to building energy resilience, can be viewed and assessed in different ways depending on stakeholder interests and use cases. This calls for a suite of metrics, and indeed it may not be possible or desirable to try and define a single metric for all these use cases. One apparent gap, vis-a-vis building energy resilience, is the emerging need for an aggregate measure of building energy resilience that can be used by owners, investors, operators. While passive survivability is a step in this direction, it is a technical metric that is more oriented towards the design community. In the next section, we build on the concept of passive survivability to propose an aggregate metric for building energy resilience that is targeted towards assessing it from the stance of business continuity for commercial buildings such as offices and retail facilities.

3. Proposed Metric for Energy Resilience in Office Buildings There are long-standing existing metrics and criteria to evaluate indoor environmental conditions for building occupants. Widely accepted guidance in this area include ASHRAE Standards 55 [33] for thermal comfort, 62.1 and 62.2 [34,35] for ventilation, and 90.1 [36] for the visual environment. While these are important constituent factors of energy re- silience, they are not in and of themselves explicitly configured as resilience metrics. They are generally calculated for a single point in space and time. Building-level resilience requires a cumulative measure integrated over space and time (e.g., total degree hours outside of thermal comfort range). We sought to develop an aggregate energy resilience metric that incorporates multiple constituent indoor environmental quality (IEQ) factors (including thermal comfort, visual comfort, ventilation), thereby providing stakeholders with a straightforward assessment of building energy resilience during a power outage. Buildings 2021, 11, 96 4 of 20

We focused our effort on office buildings, whose operations may not be critical for public safety but may still realize substantial economic consequences due to power outages. For this use case, our prior experience with industry stakeholders suggests that the metric should be relatively easy to comprehend, and should not require significant data, expertise and effort to compute. We considered two methodological approaches for defining this new building level energy resilience metric: (a) weighted scoring; and (b) productivity impact. In the weighted scoring approach, the metric is essentially a weighted sum of the individual constituent IEQ factors, normalized to a common scale for summation. The weights for each constituent IEQ factor could be varied based on the priorities of the stakeholders. The advantage of this approach is that the aggregate metric directly uses well-established measurable IEQ factors. However, the disadvantages are that the weighting is subjective, and a weighted score itself is an abstract quantity that is not inherently meaningful. The second approach we considered was to develop a metric that more directly captures productivity impact, specifically productivity lost during a power outage. This would be more meaningful for the end-users and could be more easily converted into economic impacts. Accordingly, we propose an impact-driven energy resilience metric of “occupant hours lost” (OHL) as a means to measure the business productivity lost as the result of a power outage [37]. OHL may be an absolute value (number of occupant-hours lost over a given time period) or proportional (percentage of normal occupancy lost). For example, an office building with 100 occupants working 40 h a week would have a total of 4000 occupant hours per week under normal conditions. If a power outage made the building unusable for 50 occupants for 20 h over the course of a week, the OHL would be 1000 occupant hours or 25%. The primary appeal of this metric is that it is conceptually simple and can be easily understood by building owners and occupants. It can be translated into economic impact by assigning a monetary value to each occupant hour. Additionally, it can be computed at different levels of spatial or temporal resolution (e.g., OHL for one floor or section of a building, OHL for a 3-h power outage during a summer heat event, etc.). While conceptually simple, the key methodological consideration for computing OHL are the criteria used to determine when a space is no longer usable by the occupant. Simply using the comfort criteria for normal occupancy would be unnecessarily stringent, since most occupants would be willing to tolerate less than comfortable conditions for limited periods of time, especially under exceptional circumstances such as a power outage. Based on our literature review, we defined the tolerance criteria for the standard effective temperature (SET) (SET is the temperature of an imaginary environment with 50% relative humidity, average airspeed less than 0.1 m/s, and mean radiant temperature equal to air temperature [33]). It is used to represent thermal sensation [38] as a proxy for thermal comfort. CO2 concentration is used as a proxy for ventilation, and illuminance as a proxy for visual comfort. These criteria, shown in Table1, are based on existing standards. Note that there are a maximum and minimum as well as a time-weighted tolerance limit within that range. A space would be considered unusable whenever tolerance criteria are not met for a given time interval, and the total occupant-hours in that space over that time period would be considered lost. Users may compute OHL based on each individual IEQ factor or multiple factors simultaneously. We would note that these criteria may not be universally acceptable and may need to be adjusted based on use cases and stakeholder priorities. Our review of the literature on comfort criteria showed a need for further research on human tolerance of uncomfortable indoor environmental conditions and how human physiology and behavioral aspects affect adaptation to these indoor conditions [39], albeit a topic that is largely beyond the scope of building science research, per se. Nonetheless, the criteria presented below serve as a starting point for illustrating the use of OHL. Our criteria for occupancy did not include domestic hot water. As such, domestic hot water in offices is typically needed only for handwashing and dishwashing in kitchenettes (toilets and urinals do not need hot water). Our premise is that in a critical event, occupants will be able to tolerate unheated water for handwashing and dishwashing. Buildings 2021, 11, 96 5 of 20

Table 1. Criteria for calculating OHL based on standard effective temperature, CO2, and illuminance.

IEQ Factor Criteria Basis Max 240 ◦C SET degree-hours between 30–39.4 ◦C Thermal-SET [9] Max 120 ◦C SET degree-hours between 4.4–12.2 ◦C

Ventilation-CO2 Max 40,000 ppm-hours over 8 h, never to exceed 30,000 ppm [40,41] Visual-Illuminance Min 150 lux; 100–150 lux for 1 h max per day [36]

4. How the Metric Performs: A Simulation Analysis 4.1. Approach We used energy simulation to understand and illustrate how the OHL metric varies due to different building characteristics, across different climate zones and seasons. Addi- tionally, the simulations were used to generate a dataset to develop a simple predictive model for calculating OHL based on building characteristics (described in the next section). We used the US Department of Energy (DOE) medium office prototype model compli- ant with ASHRAE 90.1-2007 [42] as the starting point for our analysis. Figure1 shows the geometry and floor plan for the prototype model, which has a total floor area of 4980 sq.m, three floors, and a rectangular floor plan with an aspect ratio of 1.5. We used a detailed zoning version of the model [43] that has more realistic thermal zoning than the standard prototype model, which only has five zones per floor. The energy models with detailed office zoning are available for OpenStudio energy modeling environment [44]. The detailed Buildings 2021, 11, x FOR PEER REVIEWzoning version has 65 zones, allowing a more fine-grained assessment of OHL variations6 of 23

in different parts of the building.

FigureFigure 1.1. FloorFloor plan plan and and geometry geometry of of the the DOE DOE medium medium office office 90.1-2007 90.1-2007 prototype prototype model model with with de- tailed zoning. detailed zoning.

WeWe thenthen conductedconducted aa parametric analysis for for three three climates climates and and 10 10 building building charac- char- acteristicsteristics related related to tothe the envelope envelope and and occupancy. occupancy. The The three three climates climates were were hot-humid hot-humid rep- representedresented by byHouston, Houston, Texas; Texas; warm-marine warm-marine represented represented by San by San Franci Francisco,sco, California; California; and andcold-humid cold-humid represented represented by Chicago, by Chicago, Illinois. Illinois. Table Table2 shows2 shows the list the of listparameters of parameters and the andrange the of range values of for values each. for The each. ranges The rangeswere de weretermined determined based on based a review on a review of the ofvalues the valuesused in used various in various vintages vintages of DOE of DOEprototype prototype models models [45] and [45] reference and reference models models [46]. [ 46The]. Theparameter parameter values values for forwindows, windows, wall wall insulation, insulation, and and roof roof insulation insulation varied varied by by climate climate to toaccount account for for different different construction construction practices practices in those in those locations. locations. The ranges The ranges for other for param- other parameterseters such as such occupant as occupant density density and plug and loads plug were loads the were same the across same climate across climate zones. HVAC zones. HVACand lighting and lighting characteristics characteristics are not are relevant not relevant since the since assumption the assumption is that isthere that is there no power is no available to run these systems. Since our use case is to assess resilience for business conti- nuity, we included plug loads under the assumption that they could be operated with battery power or onsite non-grid sources.

Table 2. Parameter variations of building characteristics. V1–V4 indicate the discrete values that each parameter can have in this analysis.

Houston San Francisco Chicago

Parameter Unit V1 V2 V3 V4 V1 V2 V3 V4 V1 V2 V3 V4

Window- to-wall ra- - 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 tio

U-Value (W/m2- 2.245 2.254 2.969 5.351 2.245 2.399 2.969 5.351 2.067 2.245 2.969 2.969 K) Window glazing SHGC 0.17 0.27 0.45 0.55 0.27 0.45 0.58 0.71 0.27 0.45 0.50 0.62 type Visible trans- 0.21 0.40 0.45 0.53 0.40 0.53 0.65 0.74 0.40 0.53 0.58 0.66 mittance Buildings 2021, 11, 96 6 of 20

power available to run these systems. Since our use case is to assess resilience for business continuity, we included plug loads under the assumption that they could be operated with battery power or onsite non-grid sources.

Table 2. Parameter variations of building characteristics. V1–V4 indicate the discrete values that each parameter can have in this analysis.

Houston San Francisco Chicago Parameter Unit V1 V2 V3 V4 V1 V2 V3 V4 V1 V2 V3 V4 Window-to-wall - 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 0.2 0.3 0.4 0.5 ratio U-Value (W/m2-K) 2.245 2.254 2.969 5.351 2.245 2.399 2.969 5.351 2.067 2.245 2.969 2.969 Window glazing SHGC 0.17 0.27 0.45 0.55 0.27 0.45 0.58 0.71 0.27 0.45 0.50 0.62 type Visible transmittance 0.21 0.40 0.45 0.53 0.40 0.53 0.65 0.74 0.40 0.53 0.58 0.66 Wall insulation U-Value (W/m2-K) 1.29 0.85 0.7 0.51 1.26 0.70 0.51 0.47 0.88 0.47 0.38 0.33 Wall reflectance - 0.22 0.3 0.5 0.7 0.22 0.3 0.5 0.7 0.22 0.3 0.5 0.7 Roof insulation U-Value (W/m2-K) 0.57 0.37 0.28 0.23 0.57 0.37 0.28 0.23 0.4 0.35 0.28 0.18 Roof reflectance - 0.3 0.55 0.7 0.8 0.3 0.55 0.7 0.8 0.3 0.55 0.7 0.8 Occupancy density ft2/person 130 200 300 400 130 200 300 400 130 200 300 400 Elec Plug and W/ft2 1.25 1 0.75 0.5 1.25 1 0.75 0.5 1.25 1 0.75 0.5 Process Orientation Degrees 0 45 90 - 0 45 90 - 0 45 90 - Infiltration 10−3 m3/s-m2 0.569 0.797 1.024 1.133 0.569 0.797 1.024 1.133 0.569 0.797 1.024 1.133

We used a quasi-Monte Carlo approach for creating parametric cases. This approach is well-suited to this analysis because buildings can have any combination of these pa- rameter values and it is not feasible to model all permutations and combinations. We set up a simulation framework that generated parametric cases by randomly selecting one parameter value from the list of values for each parameter. Each parameter value was selected independently of other parameter values (However, note that window glazing type properties (U-value, SHGC, visible transmittance) were not varied independently. Rather, the glazing type itself was treated as the variable). We generated 500 parametric cases for each climate (We determined 500 simulations to be adequate as follows: after each additional parametric simulation, we calculated the mean of the distribution of site energy. When the standard error of the mean fell below a threshold, we determined that additional parametric simulations were not required). For each climate and for each parametric case, we ran the simulation and computed OHL for power outage events for five week-long periods with different outdoor tempera- ture conditions, using the TMY weather files for the representative locations. We selected these “weather weeks” based on the average temperature from 8 a.m.–6 p.m. for each week: • Hot weather week: the week with highest average temperature. • Cold weather week: the week with lowest average temperature. • Mild weather week: the week with the median average temperature. • Cool weather week: the week with 25th percentile of average temperature. • Warm weather week: the week with 75th percentile of average temperature. In each parametric simulation run, we ran the building with normal operations for the week prior to the weather week before “shutting off” HVAC and lighting for the weather week. This ensured that any effects from normal operations in the prior week would be accounted for in the weather week. We computed four OHL metrics from the simulation output for each parametric case, using the criteria described earlier: Buildings 2021, 11, 96 7 of 20

• Thermal OHL was calculated from the hourly standard effective temperature (SET) and occupancy in each zone. It represents the building’s ability to maintain thermal habitability without HVAC systems. • Visual OHL was calculated from hourly illuminance and occupancy in each zone. It represents the building’s ability to provide adequate . The illuminance was calculated at a distance of 3 m from the window. (Illuminance is 0 lux in zones without windows.) • Ventilation OHL was calculated from the hourly CO2 concentration and occupancy in each zone. It represents the building’s ability to maintain tolerable CO2 levels without mechanical ventilation. • Overall, OHL was calculated using hourly SET, illuminance, CO2 concentration, and occupancy in each zone. It represents the building’s ability to maintain overall indoor environmental quality without active HVAC and electrical lighting. OHL was calculated for each hour for each zone and then aggregated to compute the building level OHL for each weather week.

4.2. Results and Discussion Figures2–5 show the thermal, visual, ventilation, and overall OHL, respectively. Each chart shows the OHL for the five event weeks. The OHL range for each event week is represented by a box plot showing the median, 25th, and 75th percentile (lower and upper bound of the box) and 5th and 95th percentile (lower and upper bounds of the line). A few key observations: • Thermal OHL: Thermal OHL was highest in the hot weather week for all three locations and generally increased from cold to hot weather weeks. There was a wide range on OHL across weather weeks-about 60% in Houston and Chicago and 40% in San Francisco, which has a milder climate. Thermal OHL was low in cold and cool weather weeks, which could be attributed to solar gain and internal loads. The 5th–95th percentile range of OHL is generally consistent at about 20%. • Visual OHL: In all locations, the lower bound was generally about 20% OHL. This was due to the internal zones that do not receive any daylight. OHL was higher in cool and cold weeks, which can be attributed to less daylight in winter. • Ventilation OHL: There was very little variation across locations, weather weeks and within weather weeks. This was somewhat to be expected as the only parameters affecting CO2 level in our simulation model are the rate and occupant density. • Overall OHL: This takes into account the combined effect of SET, illuminance, and CO2 criteria. As a result, the overall OHL ranges are higher than with just the individual criteria. The ranges were fairly consistent across the different climates. Lower bounds are generally around 50%. Buildings 2021, 11, x FOR PEER REVIEW The range of variation of the OHL metric suggests that it is broadly responsive9 andof 23

sensitive to weather, climate, and building characteristics; furthermore, it can be simulated and calculated with well-established existing building energy simulation approaches and tools.

(a) (b) (c)

FigureFigure 2. 2.Thermal Thermal OHL OHL for for Houston Houston (a (),a), San San Francisco Francisco (b (),b), Chicago Chicago (c ().c).

(a) (b) (c) Figure 3. Visual OHL for Houston (a), San Francisco (b), Chicago (c).

(a) (b) (c) Figure 4. Ventilation OHL for Houston (a), San Francisco (b), Chicago (c).

(a) (b) (c) Figure 5. Overall OHL for Houston (a), San Francisco (b), Chicago (c).

Finally, we would note that OHL varied significantly across different zones in the building. For example, Figure 6 shows the thermal OHL in different zones for a hot weather week in Houston, which ranges from 6–92%. While our analysis and results in this paper focus on building level OHL, some stakeholders may be interested in analyzing Buildings 2021, 11, x FOR PEER REVIEW 9 of 23 Buildings 2021, 11, x FOR PEER REVIEW 9 of 23 Buildings 2021, 11, x FOR PEER REVIEW 9 of 23

(a) (b) (c) (a) (b) (c) Buildings 2021, 11, 96 8 of 20 Figure 2. Thermal OHL for Houston (a), San Francisco (b), Chicago (c). Figure 2. Thermal OHL for Houston (a), San Francisco (b), Chicago (c).

(a) (b) (c) (a) (b) (c) Figure 3. Visual OHL for Houston (a), San Francisco (b), Chicago (c). FigureFigure 3. Visual 3. Visual OHL OHL for for Houston Houston (a), ( Sana), San Francisco Francisco (b), ( Chicagob), Chicago (c). (c).

(a) (b) (c) (a) (b) (c) Figure 4. Ventilation OHL for Houston (a), San Francisco (b), Chicago (c). FigureFigure 4. Ventilation 4. Ventilation OHL OHL for Houstonfor Houston (a), ( Sana), San Francisco Francisco (b), ( Chicagob), Chicago (c). (c).

(a) (b) (c) (a) (b) (c) FigureFigure 5. Overall 5. Overall OHL OHL for for Houston Houston (a), ( Sana), San Francisco Francisco (b), (b Chicago), Chicago (c). (c). Figure 5. Overall OHL for Houston (a), San Francisco (b), Chicago (c). TheFinally, results we also would show note the value that OHL of multiple varied OHLsignificantly metrics. across While di overallfferent OHL zones repre- in the Finally, we would note that OHL varied significantly across different zones in the sentsbuilding. the “bottom For example, line” in termsFigure of 6 building shows usability,the thermal the constituentOHL in different metrics zones suggest for how a hot building. For example, Figure 6 shows the thermal OHL in different zones for a hot toweather prioritize week interventions. in Houston, For which example, ranges consider from 6–92%. cold and While cool our weather analysis weeks, and results where in weather week in Houston, which ranges from 6–92%. While our analysis and results in thermalthis paper OHL focus is low. on The building overall level OHL OHL, is high some primarily stakeholders due to may high be visual interested OHL. Therefore,in analyzing limitedthis paper back-up focus power on building used for level lighting OHL, could some significantly stakeholders lower may visual be interested OHL and in therebyanalyzing improve overall OHL. Finally, we would note that OHL varied significantly across different zones in the building. For example, Figure6 shows the thermal OHL in different zones for a hot weather week in Houston, which ranges from 6–92%. While our analysis and results in this paper focus on building level OHL, some stakeholders may be interested in analyzing zone level OHL to inform and prioritize building resilience interventions. OHL metrics allow for such analyses since they can be computed at various levels of spatial and temporal aggregation. Buildings 2021, 11, x FOR PEER REVIEW 10 of 23

Buildings 2021, 11, 96 zone level OHL to inform and prioritize building resilience interventions. OHL metrics9 of 20 allow for such analyses since they can be computed at various levels of spatial and tem- poral aggregation.

Figure 6. Thermal OHL in different zones for a hot weather week in Houston. Figure 6. Thermal OHL in different zones for a hot weather week in Houston.

5. Impact Impact of of Building Building Characteristics-Simplified Characteristics-Simplified Predictors 5.1. Approach Approach The previous section demonstrated how OH OHLL can be calculated using conventional building simulation approaches. However, However, in practice, such simulation is not feasible for most buildings because of the level of effort to develop simulation models, especially for existingexisting buildings where data collection is more challenging than new construction. This levellevel of of effort effort may may be be justifiable justifiable for large large or critical facilities but not for small small and and medium medium offices,offices, retail, retail, food food service, service, and and sales, sales, etc. etc. For For such such buildings, buildings, owners owners and and operators, operators, in- suranceinsurance providers, providers, and and other other stakeholders stakeholders need need simple simple ways ways to assess to assess resilience resilience and iden- and tifyidentify opportunities opportunities to improve to improve it. it. Toward that end, we sought to identify whether OHL impacts could be reasonably estimated using using selected selected building building characteristics characteristics that that are are relatively relatively easy easy to obtain. to obtain. We con- We ductedconducted conventional conventional multivariate multivariate regression regression analysis analysis on the on theparametric parametric simulation simulation da- taset.dataset. The The dependent dependent variable variable was was OHL. OHL. The The independent independent variables variables were were the building the building pa- rametersparameters listed listed in inTable Table 2.2 .We We conducted conducted a a regression regression analysis for eacheach locationlocation andand weather week, and for each of the the OHL OHL metrics. metrics. Using Using the the resulting resulting regression regression coefficients coefficients forfor each parameter,parameter, wewe computed computed the the incremental incremental change change in in OHL OHL for for a given a given change change in the in theparameter parameter value. value. This, This, in essence, in essence, provides provid a measurees a measure of the impactof the ofimpact changing of changing a building a buildingcharacteristic, characteristic, all else being all else equal. being We equal. computed We computed these only these for parameter only for parameter coefficients coef- that ficientswere significant that were ( psignificant< 0.05). (p < 0.05). 5.2. Results and Discussion 5.2. Results and Discussion Tables A1–A4 in the AppendixA contain results of the regression for overall OHL, Tables A1–A4 in the Appendix A contain results of the regression for overall OHL, thermal OHL, ventilation OHL, and visual OHL, respectively, showing coefficient values thermal OHL, ventilation OHL, and visual OHL, respectively, showing coefficient values and significance for each parameter for each location and weather week. Figures7–16 show and significance for each parameter for each location and weather week. Figures 7–16 the impacts of selected individual parameters on the relevant OHL metrics, only showing show the impacts of selected individual parameters on the relevant OHL metrics, only values that were statistically significant (p < 0.05). For each parameter, we calculated the showing values that were statistically significant (p < 0.05). For each parameter, we calcu- OHL impact of a unit change in the value of that parameter, simply multiplying the unit lated the OHL impact of a unit change in the value of that parameter, simply multiplying change by the regression model coefficient for that parameter. We used a unit change that thewould unit be change meaningful by the in regression the context model of the coef generalficient range for ofthat values parameter. for each We parameter. used a unit change that would be meaningful in the context of the general range of values for each parameter. Buildings 2021, 11, x FOR PEER REVIEW 11 of 23

Buildings 2021, 11, 96 10 of 20 Buildings 2021, 11, x FOR PEER REVIEW 11 of 23

(a) (b) (a) (b)

(c()c )

FigureFigure 7. 7. ImpactImpactImpact of of ofa a 0.1 a0.1 0.1 decrease decrease decrease in in window-to-wall in window-to-wall window-to-wall ratio ratio ratio (WWR) (WWR) (WWR) on overallon on overall overall (a), thermal(a (),a), thermal thermal (b), and(b (b), ), visualand and visual visual(c) OHL. (c ()c )OHL. OHL.

(a) (b) (a) (b)

Figure 8. Impact of a 0.1 decrease in SHGC on overall (a) and thermal (b) OHL. BuildingsBuildings 2021 2021, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 1212 ofof 2323 Buildings 2021, 11, x FOR PEER REVIEW 12 of 23

Buildings 2021, 11, 96 11 of 20

FigureFigure 8.8. ImpactImpact ofof aa 0.10.1 decrease decrease inin SHGCSHGC onon overalloverall ((aa)) andand thermalthermal ((bb)) OHL. OHL. Figure 8. Impact of a 0.1 decrease in SHGC on overall (a) and thermal (b) OHL.

(a) (b) (a) (b) 2 FigureFigureFigure 9. Impact 9.9. ImpactImpact of aofof 0.2 aa 0.20.2 W/m W/mW/m2-K2-K-K decrease decreasedecrease in inin window window window U-value U-valueU-value on onon overall overalloverall (a ) ((aa and)) andand thermal thermalthermal (b ( )(bb OHL.)) OHL.OHL. Figure 9. Impact of a 0.2 W/m2-K decrease in window U-value on overall (a) and thermal (b) OHL.

(a) (b) (a) (b) Figure 10. Impact of a 0.1 W/m2-K decrease in exterior wall U-value on overall (a) and thermal (b) OHL. Figure 10. Impact of a 0.1 W/m2 2-K decrease in exterior wall U-value on overall (a) and thermal (b) OHL. FigureFigure 10. 10.Impact Impact of aof 0.1 a 0.1 W/m W/m-K2-K decrease decrease in in exterior exterior wall wall U-value U-value on on overall overall (a )(a and) and thermal thermal (b )(b OHL.) OHL.

(a) (b) (a) (b)

Figure 11. Impact of a 0.1 W/m2-K decrease in roof insulation U-value on overall (a) and thermal (b) OHL. Buildings 2021, 11, x FOR PEER REVIEW 13 of 23 Buildings 2021, 11, x FOR PEER REVIEW 13 of 23 Buildings 2021, 11, 96 12 of 20

Figure 11. Impact of a 0.1 W/m2-K decrease in roof insulation U-value on overall (a) and thermal (b) OHL. Figure 11. Impact of a 0.1 W/m2-K decrease in roof insulation U-value on overall (a) and thermal (b) OHL.

(a) (b) (a) (b) FigureFigure 12. 12. Impact of a 0.1 increase in wall reflectance on overalla (a) and thermal b(b) OHL. FigureImpact 12. Impact of a of 0.1 a increase0.1 increase in wallin wall reflectance reflectance on on overall overall ( ()a and) and thermal thermal ( (b)) OHL. OHL.

(a) (b) Buildings 2021, 11, x FOR PEER REVIEW(a) (b) 14 of 23 Figure 13. Impact of a 0.1 increase in roof reflectance on overall (a) and thermal (b) OHL. FigureFigure 13. Impact 13. Impact of a of 0.1 a increase0.1 increase in roofin roof reflectance reflectance on on overall overall (a ()a and) and thermal thermal ( b(b)) OHL. OHL.

(a) (b)

FigureFigure 14. Impact 14. Impact of a 1of W/sq.m a 1 W/sq.m decrease decrease in plugin plug loads loads on on overall overall (a ()a) and and thermal thermal ((bb)) OHL.OHL.

(a) (b) Figure 15. Impact of a 0.1 decrease in glazing visible transmittance on overall (a) and visual (b) OHL.

(a) (b) Buildings 2021, 11, x FOR PEER REVIEW 14 of 23

Buildings 2021, 11, x FOR PEER REVIEW 14 of 23

Buildings 2021, 11, 96 13 of 20

(a)( a) ((bb)) FigureFigure 14. 14. Impact Impact of ofa 1a W/sq.m1 W/sq.m decrease decrease in in plug plug loads loads on on overall overall ( (aa)) and and thermalthermal ((b)) OHL.

(a)( a) ((bb)) FigureFigureFigure 15. 15.Impact 15. Impact Impact of of a ofa 0.1 0.1 a decrease0.1 decrease decrease in in glazing in glazing glazing visible visible visible transmittance transmittance transmittance on on on overall overall overall ( a ((a)a))and andand visual visualvisual ((bb)) OHL.OHL.

Buildings 2021, 11, x FOR PEER REVIEW 15 of 23

(a) (b) (a) (b)

(c)

3 2 Figure 16. Impact of a 0.0001Figure m3/s-m 16.2 decrease Impact of in ainfiltration 0.0001 m /s-m rate decrease on overall in ( ainfiltration), thermal rate (b) and on overall ventilation (a), thermal (c) OHL. (b) and ventilation (c) OHL.

The impacts vary considerably by location as well as weather week. We offer the following key observations: • For WWR, as expected, visual OHL increases while thermal OHL generally decreases with a decrease in WWR. But the impact on visual OHL is an order of magnitude higher than the impacts on thermal OHL, especially in cool and cold weeks, and this, in turn, is reflected in the overall OHL. For example, in Houston WWR impact on thermal OHL ranges from about −2.6% to +0.4%, while WWR impact on visual OHL ranges from about 0.2 to 17.6%. • Decreasing SHGC by 0.1 lowers thermal OHL by 1.8 to 3.3% in hot and warm weather weeks. • Increasing wall reflectance and roof reflectance have approximately equivalent im- pacts on thermal OHL and have minimal if any impact on overall OHL. • Interestingly, reducing the U-value (i.e., increasing the insulation) of windows, walls, and roofs increases thermal OHL in cooler weather weeks-possibly because of the reduced ability to dissipate internal and solar gains when outdoor temperatures are lower. • As expected, a 0.1 decrease in visible transmittance significantly impacts visual OHL and overall OHL, with increasing impacts in cool and cold weeks (i.e., fall and win- ter). • Lowering plug loads by 11 W/sq.m (approximately 10% of typical office plug load values) reduces overall OHL by around 0.3–0.5% in hot and warm weeks. • Infiltration impacts appear to be minimal. • Overall, it appears the most impactful parameters are WWR, SHGC, and visible transmittance. In particular, WWR and visible transmittance significantly impact daylight availability, which in turn significantly impacts visual OHL. In the case of thermal OHL, SHGC is more impactful than wall and roof insulation, suggesting that indoor thermal conditions appear to be more influenced by solar load than the out- door temperature. The model fit for most of the metrics and weather weeks were generally good, with a few exceptions (see again Appendix A Tables A1–A4). The adjusted R2 varies from 0.59 to 0.96 for thermal OHL, 0.43–0.94 for visual OHL, 0.86 to 0.97 for ventilation OHL, and 0.45–0.93 for overall OHL. The results show significant differences between the different OHL metrics. This also explains why overall OHL does not always offer intuitive or self-explanatory results. This suggests that it is important for stakeholders to evaluate metrics based on their priorities. Buildings 2021, 11, 96 14 of 20

The impacts vary considerably by location as well as weather week. We offer the following key observations: • For WWR, as expected, visual OHL increases while thermal OHL generally decreases with a decrease in WWR. But the impact on visual OHL is an order of magnitude higher than the impacts on thermal OHL, especially in cool and cold weeks, and this, in turn, is reflected in the overall OHL. For example, in Houston WWR impact on thermal OHL ranges from about −2.6% to +0.4%, while WWR impact on visual OHL ranges from about 0.2 to 17.6%. • Decreasing SHGC by 0.1 lowers thermal OHL by 1.8 to 3.3% in hot and warm weather weeks. • Increasing wall reflectance and roof reflectance have approximately equivalent impacts on thermal OHL and have minimal if any impact on overall OHL. • Interestingly, reducing the U-value (i.e., increasing the insulation) of windows, walls, and roofs increases thermal OHL in cooler weather weeks-possibly because of the reduced ability to dissipate internal and solar gains when outdoor temperatures are lower. • As expected, a 0.1 decrease in visible transmittance significantly impacts visual OHL and overall OHL, with increasing impacts in cool and cold weeks (i.e., fall and winter). • Lowering plug loads by 11 W/sq.m (approximately 10% of typical office plug load values) reduces overall OHL by around 0.3–0.5% in hot and warm weeks. • Infiltration impacts appear to be minimal. • Overall, it appears the most impactful parameters are WWR, SHGC, and visible transmittance. In particular, WWR and visible transmittance significantly impact daylight availability, which in turn significantly impacts visual OHL. In the case of thermal OHL, SHGC is more impactful than wall and roof insulation, suggesting that indoor thermal conditions appear to be more influenced by solar load than the outdoor temperature. The model fit for most of the metrics and weather weeks were generally good, with a few exceptions (see again AppendixA Tables A1–A4). The adjusted R 2 varies from 0.59 to 0.96 for thermal OHL, 0.43–0.94 for visual OHL, 0.86 to 0.97 for ventilation OHL, and 0.45–0.93 for overall OHL. The results show significant differences between the different OHL metrics. This also explains why overall OHL does not always offer intuitive or self-explanatory results. This suggests that it is important for stakeholders to evaluate metrics based on their priorities. For example, some owners may primarily be interested in reducing thermal OHL, on the premise that in a power outage, they can use some level of battery-powered lighting or consolidate building activities in daylit spaces. A key limitation of these results is that geometry (shape and surface to volume ratio) was not a variable in the simulation dataset used for the analysis. Nevertheless, for buildings with similar rectangular geometry, the regression shows promise as a simple means to assess and screen for resilience, analogous to energy benchmarking. This is especially relevant for non-critical facilities where it may not be viable to conduct a rigorous energy resilience analysis using detailed building simulation.

6. Conclusions and Further Research Energy resilience planning for the built environment has largely focused on main- taining key facility operations concerning human wellbeing and survival during natural disasters. Our study contributes to the growing body of research on building resilience in two ways: • We propose “occupancy hours lost” (OHL) as a metric to capture the impact of a power outage. It can be calculated and aggregated at various levels of spatial and temporal resolution. It offers a relatively simple approach for evaluating the energy resilience of non-critical buildings, with a focus on supporting stakeholder priorities for business continuity during a power outage. Using parametric energy simulations, Buildings 2021, 11, 96 15 of 20

we illustrated how the metric varies due to different building characteristics, across different climate zones and seasons. • We developed a simple predictive model for calculating OHL based on building characteristics, using the aforementioned simulation results. This would allow a first- order coarse evaluation of building energy resilience with a relatively low data burden. There are several areas for further research: • Our simulation analysis was limited to a particular building morphology and occu- pancy characteristics. This should be expanded to represent a range of morphologies, sizes, and occupancy characteristics in order to more robustly evaluate the potential of using simple regression models to predict OHL. • Ultimately, the simulation-based datasets need to be complemented with empirical validation, which can be challenging due to the difficulty of emulating extreme events in real life. One potential approach may be to de-power a building, take measurements of indoor conditions, and compare these against the simulation results. • Another area of further work is to analyze how the accuracy of the metric varies with the quantity and quality of data input. This is especially relevant to wider application in the building industry, where it is still challenging to get even basic information on building characteristics without significant effort. Metrics that provide moderate accuracy with low data burden are much more likely to be widely accepted and used than high fidelity metrics that have a high data burden. • These metrics need to be field-validated by building industry stakeholders using them for actual business purposes. Finally, we would reiterate that resilience is a very broad concept and no single metric can capture the diversity of use cases. Depending on the event scenario and stakeholder priorities, the energy resilience metric presented in this paper may need to be used in conjunction with other key resilience metrics, such as structural integrity in the case of an scenario. Other use cases may call for applying the metric to aggregations of buildings, so that resilience planners and policymakers can assess energy resilience at the community scale.

Author Contributions: Conceptualization, P.M.; methodology, P.M., and L.S.; formal analysis, P.M., L.S., and T.W.; writing—original draft preparation, P.M., and L.S.; writing—review and editing, P.M., L.S., and S.H.L.; visualization, P.M., L.S., and T.W.; supervision, P.M.; project administration, P.M.; funding acquisition, P.M. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under U.S. Department of Energy Contract No. DE-AC02- 05CH11231. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The simulation results and the regression analysis data are available from the authors upon reasonable request. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data, in the writing of the manuscript, or in the decision to publish the results. Buildings 2021, 11, 96 16 of 20

Appendix A Table A1. Overall OHL Regression results.

Window Window Wall Wall Roof Roof Occupant Plug Load Case (Intercept) WWR SHGC Orientation Infiltration Adj. R2 U-Value vis Trans U-Value Reflectance U-Value Reflectance Density Density HO_hot 0.83408 0.03258 0.01388 −0.07762 −0.02213 −0.00011 0.03387 −42.78699 0.45 HO_warm 0.92863 −0.2135 0.01243 −0.18979 −0.02098 −0.00006 0.03733 −52.55214 0.60 HO_mild 1.08953 −0.52308 −0.32909 −0.02642 −0.03222 −0.04184 0.04 −75.51234 0.66 HO_cool 1.24251 −0.94812 −0.14597 −0.49549 −0.02693 0.0002 −54.39543 0.74 HO_cold 1.45032 −1.30297 −0.20264 −0.61161 0.00052 −62.88679 0.91 SF_hot 0.49055 0.1106 −0.00378 0.20627 −0.01798 −0.03146 −0.02909 0.00014 0.03834 −0.00011 −82.40585 0.86 SF_warm 0.47934 0.03852 −0.0039 0.14003 −0.02844 −0.01556 −0.02002 −0.019 0.00012 0.02267 −0.00006 −68.46596 0.75 SF_mild 0.54614 −0.02084 −0.00611 0.15431 −0.06185 −0.01917 −0.02193 −0.02123 0.00014 0.02662 −85.18133 0.58 SF_cool 1.18469 −0.94152 0.00917 −0.37309 0.00026 −97.10029 0.75 SF_cold 0.89833 −0.44449 −0.24912 0.00005 −91.64591 0.59 CH_hot 0.2105 0.21418 −0.02716 0.01269 −0.02258 −0.01302 −0.00004 0.04047 −47.30604 0.93 CH_warm 0.6362 0.0686 −0.00582 0.21087 −0.05392 −0.01205 −0.02251 −0.02384 0.00005 0.05084 −0.00011 −116.26643 0.80 CH_mild 0.67858 −0.23871 0.0425 −0.14708 0.00008 0.01271 −0.00011 −78.58245 0.49 CH_cool 1.20039 −1.0896 0.02222 −0.07286 −0.35689 −0.00006 0.00037 −68.84239 0.80 CH_cold 1.11705 −0.92302 0.02408 −0.07637 −0.2991 0.00024 −89.11845 0.76 Only coefficients with p <= 0.05 shown; Bold values indicate coefficients with p <= 0.001.

Table A2. Thermal OHL Regression results.

Window Window Wall Wall Roof Roof Occupant Plug Load Case (Intercept) WWR SHGC Orientation Infiltration Adj. R2 U-Value Vis Trans U-Value Reflectance U-Value Reflectance Density Density HO_hot 0.46288 0.19311 0.01085 0.17596 0.01308 0.01685 −0.03929 0.01713 −0.02466 −0.00007 0.07828 −16.13206 0.96 HO_warm 0.39134 0.1672 0.00803 0.17036 0.01103 0.00651 −0.03564 0.01578 −0.0311 −0.00002 0.10329 −31.14112 0.95 HO_mild 0.26186 0.0858 0.18575 −0.02694 −0.0499 −0.04036 −0.04495 0.00007 0.12178 −0.00034 −36.94327 0.92 HO_cool 0.16342 0.04988 −0.00556 0.17479 −0.02755 −0.04252 −0.03851 −0.0349 0.00014 0.09769 −0.00011 −44.32564 0.95 HO_cold 0.06712 −0.01553 −0.00668 0.07686 −0.02687 −0.01709 −0.02209 −0.00816 0.00002 0.04315 −0.00019 −23.56909 0.80 SF_hot 0.15529 0.21074 −0.00787 0.31341 0.04525 −0.02816 −0.05604 −0.01564 −0.06407 0.00022 0.10004 −0.00009 −71.31831 0.92 SF_warm 0.0463 0.16941 −0.01434 0.32515 0.05845 −0.04158 −0.06122 −0.02708 −0.06222 0.00021 0.08901 −67.35553 0.93 SF_mild 0.10439 0.15976 −0.01603 0.31604 0.05331 −0.04013 −0.05767 −0.02539 −0.06465 0.00023 0.09244 0.00004 −66.50788 0.94 Buildings 2021, 11, 96 17 of 20

Table A2. Cont.

Window Window Wall Wall Roof Roof Occupant Plug Load Case (Intercept) WWR SHGC Orientation Infiltration Adj. R2 U-Value Vis Trans U-Value Reflectance U-Value Reflectance Density Density SF_cool 0.09911 −0.03505 −0.02001 0.11755 0.02586 −0.03813 −0.01628 −0.04688 −0.01418 0.00004 0.067 −0.00021 −31.1346 0.91 SF_cold 0.16269 −0.0154 0.27486 0.03355 −0.04017 −0.03666 −0.04179 −0.01769 0.00013 0.05636 −0.00093 −26.46278 0.86 CH_hot 0.4202 0.25897 0.25586 −0.01936 0.01853 −0.03022 0.01548 −0.02228 0.00002 0.07217 0.00004 −42.18851 0.93 CH_warm 0.29996 0.19879 −0.01792 0.3201 −0.0185 −0.03904 −0.04701 0.0001 0.11495 −0.00015 −82.49559 0.90 CH_mild 0.09487 0.11318 −0.03483 0.31584 −0.06512 −0.0325 −0.08057 −0.02433 0.00017 0.08979 −0.00049 −56.3568 0.91 CH_cool 0.01239 0.00808 −0.00243 0.01441 −0.00385 0.00003 0.00301 −0.00004 −5.49333 0.59 CH_cold 0.01152 −0.00068 0.00157 −0.00087 0.00039 0.00003 0.00067 0 −0.64141 0.93 Only coefficients with p <= 0.05 shown; Bold values indicate coefficients with p <= 0.001.

Table A3. Ventilation OHL Regression results.

Window Window Wall Wall Roof Roof Occupant Plug Load Case (Intercept) WWR SHGC Orientation Infiltration Adj. R2 U-Value Vis Trans U-Value Reflectance U-Value Reflectance Density Density HO_hot 0.51231 −0.00222 0.01725 0.00018 −153.14466 0.92 HO_warm 0.41364 0.00018 −121.63163 0.97 HO_mild 0.43035 0.00019 −118.99631 0.97 HO_cool 0.37269 0.00007 −114.66429 0.93 HO_cold 0.37384 0.00639 0.00008 −118.26842 0.95 SF_hot 0.35438 0.00011 −0.00002 −88.57826 0.94 SF_warm 0.32633 0.00058 0.00008 −0.00185 −72.60319 0.92 SF_mild 0.36495 0.0001 −109.3139 0.94 SF_cool 0.35865 0.00006 −103.42958 0.91 SF_cold 0.37906 0.00113 −0.00806 0.00012 0.00003 −100.15798 0.93 CH_hot 0.35451 −0.00444 0.00012 −87.22699 0.87 CH_warm 0.41193 0.00016 −131.37983 0.96 CH_mild −0.00246 0.0001 −83.56577 0.92 CH_cool 0.32165 0.00737 0.0022 0.00003 −79.93948 0.86 CH_cold 0.36489 −0.00368 0.00008 −101.5246 0.92 Only coefficients with p <= 0.05 shown; Bold values indicate coefficients with p <= 0.001 Buildings 2021, 11, 96 18 of 20

Table A4. Visual OHL Regression results.

Window Window Wall Wall Roof Roof Occupant Plug Load Case (Intercept) WWR SHGC Orientation Adj. R2 U-Value Vis Trans U-Value Reflectance U-Value Reflectance Density Density HO_hot 0.68788 −0.34306 0.01929 −0.3148 −0.29769 −0.0003 0.43 HO_warm 1.02647 −0.88035 0.01222 −0.28549 −0.5045 −0.00027 0.78 HO_mild 1.11223 −0.95341 −0.20389 −0.59517 −0.00025 0.00025 0.70 HO_cool 1.35684 −1.389 −0.28819 −0.70917 −0.00022 0.00051 0.75 HO_cold 1.58249 −1.75991 −0.26366 −0.82182 −0.00017 0.00078 0.91 SF_hot 0.35566 −0.04015 0.00182 0.01444 −0.05929 −0.00025 0.85 SF_warm 0.3677 −0.05239 0.00221 0.02056 −0.07871 −0.00025 0.79 SF_mild 0.42582 −0.13533 0.00456 −0.14755 −0.00024 0.00009 0.54 SF_cool 1.20394 −1.22743 0.0119 −0.49739 −0.00022 0.00033 0.78 SF_cold 0.82707 −0.64687 0.00867 −0.34265 −0.00025 0.64 CH_hot 0.32589 −0.01696 0.00288 −0.01717 −0.00025 0.94 CH_warm 0.38083 −0.09991 0.00875 −0.07705 −0.00025 0.76 CH_mild 0.56812 −0.38237 0.0189 −0.21743 −0.00025 0.60 CH_cool 1.21665 −1.34897 0.02706 −0.08916 −0.42726 −0.00021 0.00043 0.80 CH_cold 1.10494 −1.20215 0.03392 −0.10789 −0.384 −0.00022 0.00037 0.78 Only coefficients with p <= 0.05 shown; Bold values indicate coefficients with p <= 0.001 Buildings 2021, 11, 96 19 of 20

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